New metrics are introduced for tracking pixel loss and duplication during the transformation of discrete raster data sets by map projection. The metrics, , successfully measure pixel loss and pixel duplication, respectively, throughout the spatial realm and provide evidence of the property of equal area. are applied to the examination of world equal-area map projections. Traditional map projection distortion evaluation addresses scale, area, shape, and directional distortion, which is appropriate to point-by-point analytical projection methods used for vector data. provide an additional means for evaluating map projection distortion for discrete raster data. Data producers and data users, including researchers and policy makers, are often unaware that the choice of a map projection may affect the content of data sets and, possibly, research results. Pixel duplication may be reversed in some cases, but lost pixels mean that data has been lost forever. The results of this work indicate the need for a change in cartographic recommendations for selecting global raster data map projections. The Sinusoid projection, with the greatest angular distortion of the projections studied, would be an unlikely choice for a global equal-area data set, but it exhibits no pixel loss or duplication. Source.